Question

given is the right triangle TUV with altitude UO. Apply the Pythagorean theorem and similar triangles to find the length of line OV

side lengths
UT = 4
TO = 1


15−−√
square root of 15

15
15

215−−√

Answer 1

Assume U is the right angle and UO is the altitude to the hypotenuse TV. Let OV = x. A standard result (from similar triangles) is

UT^2 = TO · TV.

Here UT = 4 and TO = 1, so
16 = 1 · TV ⇒ TV = 16.

Thus OV = TV − TO = 16 − 1 = 15.